Solving a system of ODE with BCs

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Elia Paini 2021-4-20

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评论： Elia Paini 2021-4-24

Hi, I'm trying to solve a system of 2 ODE with boundary conditions.

The integration variable is r, which is the sferical coordinate (radius of a sphere). At the end of the simulation I should get the values of A and B as a functions of r, where the maximum value of r is 1.

k,c,a,b are constants.

The system is as follows:

Equations:

BCs:

I converted the system to first order one, as follows:

Equations:

BCs:

Y3(0)=Y4(0)=0

Y1(1)=a

Y2(1)=b

How can I solve it?

Thank you!

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采纳的回答

Divija Aleti 2021-4-23

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Hi Elia,

The following link gives an example of how to solve a system of two first-order differential equations with boundary conditions. Similarly, you can solve for your converted system of four first order differential equations.

Solve a System of Differential Equations

Hope this helps!

Regards,

Divija